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Tokyo Probability Seminar
Seminar information archive ～01/12｜Next seminar｜Future seminars 01/13～
| Date, time & place | Monday 16:00 - 17:30 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Makiko Sasada, Shuta Nakajima, Masato Hoshino |
Next seminar
2026/01/14
15:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Xia Chen (University of Tennessee) 15:00-16:00
Hyperbolic Anderson equations and Brownian intersection local times
Moderate deviations for the capacity of the random walk range
Xia Chen (University of Tennessee) 15:00-16:00
Hyperbolic Anderson equations and Brownian intersection local times
[ Abstract ]
An idea recently merged from the investigation of hyperbolic Anderson equations is
to represent the chaos expansion of the solution in terms of Brownian intersection local
times. In this talk, I will address effeteness, current state, potentials and challenge about
this method.bPart of the talk comes from the work joined with Yaozhong Hu
Jiyun Park (Stanford University) 16:30-17:30An idea recently merged from the investigation of hyperbolic Anderson equations is
to represent the chaos expansion of the solution in terms of Brownian intersection local
times. In this talk, I will address effeteness, current state, potentials and challenge about
this method.bPart of the talk comes from the work joined with Yaozhong Hu
Moderate deviations for the capacity of the random walk range
[ Abstract ]
It is known that the capacity of the range of a random walk in d dimensions behaves similarly to the volume of the random walk in d-2 dimensions. In this talk, we extend this analogy to the moderate deviations of the capacity in dimension 5. In particular, we demonstrate that the large deviation principle transitions from a Gaussian tail to a non-Gaussian tail depending on the deviation scale. We also improve previously known results for dimension 4. Based on joint work with Arka Adhikari.
It is known that the capacity of the range of a random walk in d dimensions behaves similarly to the volume of the random walk in d-2 dimensions. In this talk, we extend this analogy to the moderate deviations of the capacity in dimension 5. In particular, we demonstrate that the large deviation principle transitions from a Gaussian tail to a non-Gaussian tail depending on the deviation scale. We also improve previously known results for dimension 4. Based on joint work with Arka Adhikari.
